Limit cycles, invariant meridians and parallels for polynomial vector fields on the torus |
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| Authors: | Jaume Llibre,Joã o C. Medrado |
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| Affiliation: | aDepartament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain;bInstituto de Matemática e Estatística, Universidade Federal de Goiás, 74001-970 Goiânia, Goiás, Brazil |
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| Abstract: | We study the polynomial vector fields of arbitrary degree in R3 having the 2-dimensional torus invariant by their flow. We characterize all the possible configurations of invariant meridians and parallels that these vector fields can exhibit. Furthermore we analyze when these invariant either meridians or parallels can be limit cycles. |
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| Keywords: | MSC: 58F14 58F22 34C05 |
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